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The point [tex]\((12, 9)\)[/tex] is included in a direct variation. What is the constant of variation?

A. [tex]\(\frac{1}{2}\)[/tex]
B. [tex]\(\frac{3}{4}\)[/tex]
C. 1
D. 2

Sagot :

GinnyAnswer
To determine the constant of variation for a direct variation problem, we can use the relationship given by the direct variation equation:

[tex]\[ y = kx \][/tex]

Here, [tex]\( k \)[/tex] is the constant of variation. We start by solving for [tex]\( k \)[/tex] using the given point [tex]\((12, 9)\)[/tex], where [tex]\( x = 12 \)[/tex] and [tex]\( y = 9 \)[/tex].

First, we substitute the given values into the direct variation equation:

[tex]\[ 9 = k \cdot 12 \][/tex]

To isolate [tex]\( k \)[/tex], we divide both sides of the equation by 12:

[tex]\[ k = \frac{9}{12} \][/tex]

Now, simplify the fraction:

[tex]\[ k = \frac{3}{4} \][/tex]

Therefore, the constant of variation [tex]\( k \)[/tex] is [tex]\(\frac{3}{4}\)[/tex].

Given the answer choices:
- [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex]
- 1
- 2

The value of [tex]\(\frac{3}{4}\)[/tex] corresponds to the second choice.

So, the correct choice is:

[tex]\(\boxed{\frac{3}{4}}\)[/tex]
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